'\"
'\" Generated from file 'symdiff\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2010 by Kevin B\&. Kenny <kennykb@acm\&.org>
'\" Redistribution permitted under the terms of the Open Publication License <http://www\&.opencontent\&.org/openpub/>
'\"
.TH "math::calculus::symdiff" n 1\&.0\&.1 tcllib "Symbolic differentiation for Tcl"
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.SH NAME
math::calculus::symdiff \- Symbolic differentiation for Tcl
.SH SYNOPSIS
package require \fBTcl  8\&.5\fR
.sp
package require \fBgrammar::aycock  1\&.0\fR
.sp
package require \fBmath::calculus::symdiff  1\&.0\&.1\fR
.sp
\fBmath::calculus::symdiff::symdiff\fR \fIexpression\fR \fIvariable\fR
.sp
\fBmath::calculus::jacobian\fR \fIvariableDict\fR
.sp
.BE
.SH DESCRIPTION
.PP
The \fBmath::calculus::symdiff\fR package provides a symbolic differentiation
facility for Tcl math expressions\&. It is useful for providing derivatives
to packages that either require the Jacobian of a set of functions or else
are more efficient or stable when the Jacobian is provided\&.
.SH PROCEDURES
The \fBmath::calculus::symdiff\fR package exports the two procedures:
.TP
\fBmath::calculus::symdiff::symdiff\fR \fIexpression\fR \fIvariable\fR
Differentiates the given \fIexpression\fR with respect to the specified
\fIvariable\fR\&. (See \fBExpressions\fR below for a discussion of the
subset of Tcl math expressions that are acceptable to
\fBmath::calculus::symdiff\fR\&.)
The result is a Tcl expression that evaluates the derivative\&. Returns an
error if \fIexpression\fR is not a well-formed expression or is not
differentiable\&.
.TP
\fBmath::calculus::jacobian\fR \fIvariableDict\fR
Computes the Jacobian of a system of equations\&.
The system is given by the dictionary \fIvariableDict\fR, whose keys
are the names of variables in the system, and whose values are Tcl expressions
giving the values of those variables\&. (See \fBExpressions\fR below
for a discussion of the subset of Tcl math expressions that are acceptable
to \fBmath::calculus::symdiff\fR\&. The result is a list of lists:
the i'th element of the j'th sublist is the partial derivative of
the i'th variable with respect to the j'th variable\&. Returns an error if
any of the expressions cannot be differentiated, or if \fIvariableDict\fR
is not a well-formed dictionary\&.
.PP
.SH EXPRESSIONS
The \fBmath::calculus::symdiff\fR package accepts only a small subset of the expressions
that are acceptable to Tcl commands such as \fBexpr\fR or \fBif\fR\&.
Specifically, the only constructs accepted are:
.IP \(bu
Floating-point constants such as \fB5\fR or \fB3\&.14159e+00\fR\&.
.IP \(bu
References to Tcl variable using $-substitution\&. The variable names
must consist of alphanumerics and underscores: the \fB${\&.\&.\&.}\fR notation
is not accepted\&.
.IP \(bu
Parentheses\&.
.IP \(bu
The \fB+\fR, \fB-\fR, \fB*\fR, \fB/\fR\&. and \fB**\fR
operators\&.
.IP \(bu
Calls to the functions \fBacos\fR, \fBasin\fR, \fBatan\fR,
\fBatan2\fR, \fBcos\fR, \fBcosh\fR, \fBexp\fR, \fBhypot\fR, \fBlog\fR,
\fBlog10\fR, \fBpow\fR, \fBsin\fR, \fBsinh\fR\&. \fBsqrt\fR, \fBtan\fR,
and \fBtanh\fR\&.
.PP
Command substitution, backslash substitution, and argument expansion are
not accepted\&.
.SH EXAMPLES
.CS


math::calculus::symdiff::symdiff {($a*$x+$b)*($c*$x+$d)} x
==> (($c * (($a * $x) + $b)) + ($a * (($c * $x) + $d)))
math::calculus::symdiff::jacobian {x {$a * $x + $b * $y}
                         y {$c * $x + $d * $y}}
==> {{$a} {$b}} {{$c} {$d}}

.CE
.SH "BUGS, IDEAS, FEEDBACK"
This document, and the package it describes, will undoubtedly contain
bugs and other problems\&.
Please report such in the category \fImath :: calculus\fR of the
\fITcllib Trackers\fR [http://core\&.tcl\&.tk/tcllib/reportlist]\&.
Please also report any ideas for enhancements you may have for either
package and/or documentation\&.
.PP
When proposing code changes, please provide \fIunified diffs\fR,
i\&.e the output of \fBdiff -u\fR\&.
.PP
Note further that \fIattachments\fR are strongly preferred over
inlined patches\&. Attachments can be made by going to the \fBEdit\fR
form of the ticket immediately after its creation, and then using the
left-most button in the secondary navigation bar\&.
.SH "SEE ALSO"
math::calculus, math::interpolate
.SH COPYRIGHT
.nf
Copyright (c) 2010 by Kevin B\&. Kenny <kennykb@acm\&.org>
Redistribution permitted under the terms of the Open Publication License <http://www\&.opencontent\&.org/openpub/>

.fi
